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Radiometric dating techniques have always been an important element in the modern Creation-evolution controversy. From the time that radioactive decay rates were first suggested as a means of measuring the age of rocks, creation-model scientists and other critical thinkers were quick to point out that because the original compositions of the rocks could not be established, the "age" as measured was actually conjecture, and without compelling scientific value. Nothing has happened to change that. However, a very clever mathematical trick called 'concordia curves' and 'isochrons' has more recently been used by geochronologists to delude themselves into thinking that they are able to find rigorous proofs for old-age in rocks through radioactive data.

These mathematical methods are indeed rigorous, and at first glance appear very compelling evidence for ancient ages. However, careful analysis discloses that there is at least one other equally valid mechanism for the source of the data, and no cogent proof that can be offered that any significant amount of any radiogenic daughter element has ever been the result of decay from the parent over long ages.

In 1981, Arndts, Overn and Kramer (1) (2) (3) published a series of papers which discussed the modern methods of radiometric dating. These methods use straight-line plots of the ratios of radioisotopes. This paper focuses on a straight-line plot called an 'isochron'.

By plotting the ratio of the daughter element to a non-radiogenic isotope vs. the ratio of the parent to the same isotope a straight line often results. An example is a plot of 87Sr/86Sr vs. 87Rb/86Sr. 87Rb decays to 87Sr by beta decay, with a half-life of 48.8 billion years.

Scientific experience tells us that when data fit on a mathematically defined curve, especially on a straight line, that there is a fundamental relationship between the data points, and that this relationship can be discovered. In this case evolutionary geochronologists presume that the relationship is the decay over time of the parent into the daughter. It follows that there is no problem in determining the original composition of daughter isotopes -- it is given by the zero intercept of the straight line. The slope of the isochron defines the age of the sample. There is furthermore no question as to whether the sample has been a "closed system" over time. If it were not, the data would not fit a straight line.

The isochron method is elegant, because it eliminates so many problems of calibration and possible error. It is essentially self-checking, because of the requirement that the data points lie on a straight line.

There is, however, the need to verify the mechanism which may have yielded the data of the straight line. There must primarily be a valid mechanism for having given parts of the rock differing initial quantities of parent isotopes, so that a plot could be made, rather than a single point.

Arndts and Overn (2) pointed out that another equally well-known mechanism, mixing of parts from other initial rocks, can give the same results. If mixing is the mechanism, the data have no time significance -- the rock could have formed yesterday.

It becomes apparent that the validation of radiometric dating is based on the premise that the earth is billions of years old. Radiometric dating can in no way constitute proof of ancient age, since any individual measurement could be due to mixing, rather than decay.

Dalrymple (4) has defended the use of isochrons over against the probability of mixing. His "proofs" of the value of the isochrons encompass five points, having varying degrees of validity.

1. The test for mixing is not conclusive. There is a test that has generally been accepted as an indication that the straight-line isotopic ratio relationship is the result of incomplete mixing of two original components (3). The test is based on the fact that two end members, mixed in differing proportions, will yield a linear relationship when plots are made of the composition of the various intermediate mixtures. Any constituent of either or both of the end members may make a suitable test (linear plot) providing the original end-member materials are themselves homogeneous, and that the constituents themselves neither vary with time nor can have entered or left the rock since the mixture was formed. If the property being plotted is a ratio of elements or isotopes, an hyperbola may result. This can sometimes be converted to a straight line by plotting the reciprocal of one of the parameters.

A linear array indicates a closed system. When a linear isochron of 87Sr/86Sr vs. 87Rb/86Sr has been obtained, it is a reasonable assumption that the system has been closed to these three isotopes, but not necessarily to any other elements. The commonly-accepted test to determine whether the linear relationship is due to two-component mixing, and to ultimately determine the composition of the end members, is to plot the 87Sr/86Sr ratio versus 1/Sr (the concentration of Strontium). Using 1/Sr rather than Sr gives a linear plot rather than an hyperbola.

Dalrymple (4) states that such a linear relationship of the isotope ratio vs. 1/Sr is "a necessary consequence of mixing, but -- not a sufficient test for mixing." Dalrymple is not accurate in the first statement. It is not a necessary consequence, but only will be true in the special circumstances that the mixing is simple mixing of only two components, and that these components were homogeneous. Mixtures of three or more components will not yield these results. The mixing must also be incomplete, as a homogeneous mixture will yield only one point, not an array.

As for its not being a sufficient test for mixing, Dalrymple points out that Rubidium and Strontium are both trace elements in the various minerals. They resemble, chemically, different elements that are natural to the minerals, so that where Strontium is slightly welcome, Ribidium is strongly rejected, and vice versa. The result is a quasi-linear relationship between Rb and Sr in the minerals, which can resemble two-component mixing in the plotting process. We concede that, in light of the above arguments, data could indeed show positive correlation to the mixing test, without mixing having been proved. It is obvious, however, that the above mechanisms involve crystal growth, and apply directly to mineral isochrons. How this may apply to whole rock is complex and will not be further discussed here except to note that rocks are a conglomerate of an indefinite number of undefined minerals, but we cannot expect that the total concentration of trace elements in the whole rock can be controlled entirely by their acceptability within the minerals.

When we suggested (3) that several published isochrons should not have been published because of positive mixing tests, we concede that, in light of the above, there was no more proof for mixing than there is for ancient age. The mixing test only indicates that the most probable mechanism for the data plotted as an isochron is simple two-part mixing, but does not constitute proof. It should also be noted that most published isochrons are whole-rock isochrons in which the mixing test has considerably greater credibility.

We perceive no comfort to the proponents of isochrons in having to discard the validity of a test for mixing. One can never trust an isochron, because mixing cannot be ruled out.

2. Mixing would require a mechanism. Dalrymple points out that mixing requires the availability of initial components, for example lava in contact with crystal rocks. He claims the greatest use of Rb-Sr isochrons, however, is in igneous rocks, "which cool from a liquid "melt. He questions the presence of end members, and notes that an end member, if injected into a melt, would not be preserved.

The plotting of the data in the form of an isochron requires finding individual samples with differing amounts of Rb, in order to have sufficient points to plot. This requires that the gross sample being analyzed be heterogeneous. "Mixing" implies homogenization, but this is not the case. What is required is imperfect mixing, to provide data points (heterogeneities). (Note that these mixing lines have no time significance.)

The mineral isochron is an elegant scheme for obtaining the required heterogeneity. Dalrymple states that "mineral composition and the sequence of mineral formation are governed by chemical laws and do not involve mixing." He is referring to the fact that as the crystals of individual minerals form, they absorb varying trace amounts of Rb and Sr, depending upon their individual chemistry. This is affected by the concentration of the trace elements, however, so that heterogeneities due to partial mixing will also affect the process.

The elegance of the mineral isochron lies in the fact that the selectivity of crystals to the trace elements provides, in the form of a well known mechanism, the required heterogeneity to make the plot.

Many of these Rb-Sr isochrons yield a time result of billions of years. But could the various strontium ratios be due to initial heterogeneities from some more recent event? Dalrymple assumes not, but there is much evidence to the contrary.

The isochron process depends on heterogeneities in Rb at the beginning. The introduction of subsequent heterogeneity would simply destroy the process. The process also depends on homogeneity in the strontium ratio at the beginning. Any initial systematic heterogeneity in the Sr ratio from partial mixing, or from any other source, will yield a fictitious isochron or mixing line, and as we have elaborated above, there is no test to rule it out.

Rb-Sr isochrons are regularly published from data obtained from the whole rock. The crystallization process cannot be depended upon here to provide the heterogeneity that occurs. (The existence of the isochron attests to heterogeneity.) If the heterogeneity is of recent origin, the isochron is unreliable. If the heterogeneity was there at the beginning, then the melt was not homogeneous, and the Sr ratios were probably also heterogeneous, defining the isochron as a mixing line.

Dalrymple has restricted his statements to mineral isochrons. It is reasonable to surmise that he is unwilling to defend the whole-rock isochron, and rightly so. The most logical mechanism for the required heterogeneity in the whole rock is partial mixing.

The evidence clearly does not support Dalrymple's claim that mixing can be ruled out on the basis that igneous rocks cooled from an homogeneous melt.

3. To have an end member with the required high 87Rb/86Sr ratio for any isochron to be due to mixing would in itself indicate the passage of billions of years. This is a conclusion based on the ancient-earth model that the isochrons are devised to prove. It is clearly begging the question.

4. If isochrons are due to mixing, roughly one-half should show a negative slope. It is probable that if all samples gathered from the field for testing by this method resulted in published curves, that a reasonably large percentage would be negative. However, since little significance is given to these "mixing lines", and because of the time and expense involved in obtaining the data, few negative-slope plots could be expected to be completed, and a much smaller number of those published. A significant sample does show up in the literature, however, which should be sufficient to satisfy a judgment that the field data satisfy this criterion.

5. There are numerous isochrons that do not conform to the test for mixing. In order to get the straight-line relationship often called an isochron, special heterogeneities must occur. These could be due to time and nuclear decay, to partial mixing, or to other processes. If it is mixing, certain special circumstances will allow it to give. the further straight-line relationship called the "mixing test".': We have already shown that the mixing test does not prove mixing, but rather shows it to be probable. However, failing the test for mixing can in no way rule out mixing.

Three-part (or more) mixtures can yield a straight-line plot of the isochron parameters, but will never conform to the "mixing test".

If we were to plot the isochron parameters from data resulting from two-part mixing of end members containing Rb and Sr, a straight line would result, as well as a straight-line mixing-test plot. If there were three-part mixing, all points on both plots would fall within a triangle, but would have no correlation. When three or more parts are mixed, if only two contain significant amounts of Sr and Rb, the isochron parameters will plot on a straight line, but any mixing test will show scatter. The reason is that isochron parameters are ratios of isotopes, which are not sensitive to dilution, whereas the mixing tests involve at least one concentration which is highly sensitive to dilution. For a sample to fail to conform to the mixing test criteria only rules out the special case of simple two-part mixing, but does not rule out mixing in general. Geochemists are also recognizing more and more the existence of multi-part mixing. (5)

Dalrymple has presented his five-part proof that isochrons have presented valid crystallization ages for the rocks. We have shown here that none of the statements represent crucial experiments which could validate the isochron over the mixing model. isochrons are not proof of ancient ages.

Geochronologists do not generally propose the isochrons as proof for ancient age, even though many others accept it as such. Each isochron, for every rock system, is carefully studied before accepting it as a true age. Mixing is only one of many valid reasons why an isochron should be suspect. Ultimate acceptance depends on the degree of fit with a large body of accepted dates. The original accepted dates were derived from the fossil record and uniformitarian assumptions, and were available from the beginning of the radiometric technology. They played an important role in this acceptance. We can therefore make a general statement that the "radiometric clock" was "calibrated" to the fossil dates.

Dalrymple,(6) elsewhere in the volume we have been discussing , says "...each different type of mineral and rock has to be tested carefully before it can be used for any radiometric dating technique." Statements referring to the need for selection abound in the literature. A common term is whether the data are "strategraphically" acceptable, referring to the fossil data.

The mineral isochrons that Dalrymple has so eloquently defended are not accorded as much credibility as the whole-rock isochrons that Dalrymple has wisely omitted from his defense. Mineral crystals have often been used in discordia analysis, another straight-line plot which is interpreted, in this case, to be a systematic open system, rather than a closed system. Discordia have been obtained from several crystals of the same mineral (7, 8) as well as from several parts of the same crystal. (9) The conclusion is that mineral crystals are not reliable closed systems. Whole rock isochrons are systematically preferred (on a superficial literature survey, approximately 10:1) over the mineral, based on the above, but primarily prompted by the better fit with accepted data. Note, however, that the mixing model is the only simple straightforward explanation for the straight-line heterogeneities in the whole rock.

Proof for the effectiveness of a technique is up to its proponents. Its critics need only to propose potential hazards. In the case of radiometric dating, the mixing model is one serious cause for doubt. The proponents of radiometric dating have still to furnish effective proof for an ancient earth.

8. Lancelot, J. et al. 1976. Uranium and Lead Isotope Dating with Grain by Grain Zircon Analysis: A Study of Complex Geological History with a Single Rock. Earth and Planetary Science Letters (Netherlands) 29:357-366.